Bayesian analysis of the piecewise diffusion decision model
Most past research on sequential sampling models of decision-making have assumed a time homogeneous process (i.e., parameters such as drift rates and boundaries are constant and do not change during the deliberation process). This has largely been due to the theoretical difficulty in testing and fitting more complex models. In recent years, the development of simulation-based modeling approaches matched with Bayesian fitting methodologies has opened the possibility of developing more complex models such as those with time-varying properties. In the present work, we discuss a piecewise variant of the well-studied diffusion decision model (termed pDDM) that allows evidence accumulation rates to change during the deliberation process. Given the complex, time-varying nature of this model, standard Bayesian parameter estimation methodologies cannot be used to fit the model. To overcome this, we apply a recently developed simulation-based, hierarchal Bayesian methodology called the probability density approximation (PDA) method. We provide an analysis of this methodology and present results of parameter recovery experiments to demonstrate the strengths and limitations of this approach. With those established, we fit pDDM to data from a perceptual experiment where information changes during the course of trials. This extensible modeling platform opens the possibility of applying sequential sampling models to a range of complex non-stationary decision tasks.
KeywordsEvidence accumulation models Non-stationary stimuli Hierarchal Bayesian inference
WRH and JST were supported by National Science Foundation Grant SES-1556325.
- Diederich, A., & Trueblood, J. (submitted). A dynamic dual process model of risky decision-making.Google Scholar
- Guo, L., Trueblood, J. S., & Diederich, A. (2015). A dual-process model of framing effects in risky choice. In Noelle, D.C., & et al (Eds.), Proceedings of the 37th annual conference of the cognitive science society (pp. 836–841). Austin, TX: Cognitive Science Society.Google Scholar
- Logan, G. D., & Burkell, J. (1986). Dependence and independence in responding to double stimulation: A comparison of stop, change, and dual-task paradigms. Journal of Experimental Psychology: Human Perception and Performance, 12(4), 549–563.Google Scholar
- Silverman, B. W. (1982). Algorithm as 176: Kernel density estimation using the fast Fourier transform. Journal of the Royal Statistical Society. Series C (Applied Statistics), 31(1), 93–99.Google Scholar
- Silverman, B. W. (1986). Density estimation for statistics and data analysis (Vol. 26). CRC Press.Google Scholar
- Tsetsos, K., Gao, J., McClelland, J. L., & Usher, M. (2012). Using time-varying evidence to test models of decision dynamics: Bounded diffusion vs. the leaky competing accumulator model. Frontiers inNeuroscience, 6.Google Scholar
- Tsetsos, K., Usher, M., & McClelland, J. L. (2011). Testing multi-alternative decision models with non-stationary evidence. Frontiers in neuroscience, 5.Google Scholar